Electrical communications systems ece 09 331 spring 2007
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Electrical Communications Systems ECE.09.331 Spring 2007. Lecture 8b March 7, 2007. Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring07/ecomms/. Plan. Analyzing FM Signals - Battle Plan!!!! Single-tone FM Bessel Functions FM Spectra

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Electrical communications systems ece 09 331 spring 2007

Electrical Communications SystemsECE.09.331Spring 2007

Lecture 8bMarch 7, 2007

Shreekanth Mandayam

ECE Department

Rowan University

http://engineering.rowan.edu/~shreek/spring07/ecomms/


Plan

  • Analyzing FM Signals - Battle Plan!!!!

    • Single-tone FM

    • Bessel Functions

    • FM Spectra

    • Power etc.

  • Digital Communications

    • Introduction

    • Digital Communications Transceiver (CODEC/MODEM)



Angle modulation systems
Angle Modulation Systems

  • Signal Representation

    • Complex Envelope

    • Time Domain Representation

  • Terminology

    • Phase Sensitivity

    • Frequency Deviation

    • Instantaneous Frequency

    • Phase & Frequency Modulation Indices

  • Phase Modulation (PM) Frequency Modulation(FM)

    Instrument Demo

    Matlab Demo:

    anglemod.m


    Analyzing fm signals battle plan

    Signals Systems

    • Time Domain

    • Complex Envelope

    • Spectrum

      • Single-tone FM

        • Narrowband FM

        • Wideband FM

          • Bessel Functions

    • Power

    Performance

    Transmitters

    Receivers

    Standards

    Modulation

    Index

    Efficiency

    Bandwidth

    Noise

    Analyzing FM Signals - Battle Plan!!!

    Instrument Demo


    Bessel s differential equation
    Bessel’s Differential Equation

    • German mathematician and astronomer Friedrich Wilhelm Bessel (1784 - 1846)

    • Discovered this equation while investigating planetary motion

    • 2nd order ODE, Nonlinear, Variable Coefficients, Homogeneous

    • Very important in applied mathematics and engineering

      • Governing equation for problems with cylindrical geometries, e.g. waveguides, vibrating strings, and …………!!!!!!!


    Bessel functions
    Bessel Functions

    Matlab Demo

    » help besselj

    BESSELJ Bessel function of the first kind.

    J = BESSELJ(NU,Z) is the Bessel function of the first kind, J_nu(Z).The order NU need not be an integer, but must be real.The argument Z can be complex. The result is real where Z is positive.

    »

    »

    »

    » x=0:0.1:10;

    » plot(x,besselj(0,x));

    » title('Bessel Function of Order Zero, J_0(x)');

    » xlabel('x');

    »


    Bessel functions1
    Bessel Functions

    Matlab Demo

    %ECOMMS Spring 07 Classroom Demo

    %S. Mandayam, ECE, Rowan University

    clear;close all;

    n=0:6;

    beta=0:0.1:10;

    Jn=besselj(n,beta');

    plot(beta',Jn);

    grid on;

    xlabel('Frequency Modulation Index: \beta');

    ylabel('J_n(\beta)');

    legend('J_0(\beta)','J_1(\beta)','J_2(\beta)',

    'J_3(\beta)','J_4(\beta)','J_5(\beta)','J_6(\beta)');

    title('J_n(\beta): Spectral Amplitudes of an FM signal at f_c \pm nf_m');

    http://engineering.rowan.edu/~shreek/spring07/ecomms/demos/besselfun.m

    Instrument Demo


    Fm signal spectrum

    J1(b)

    |S(f)| / (Ac/2)

    J2(b)

    J3(b)

    J0(b)

    0fc-3fm fc-2fm fc-fm fc fc+fm fc+2fm fc+3fm

    f

    FM Signal & Spectrum

    Single-tone FM Signal

    Single-tone FM Spectrum



    Digital communications
    Digital Communications

    • Some Milestones

      • Claude Shannon, 1948

      • X.25 (Telephony)

      • IEEE 802.3 (Ethernet)

      • ARPANET, 1969

      • IEEE 802.5 (FDDI)

      • ISO-OSI 7-layer Network Reference Model

      • CDMA

      • GSM

      • VOIP

        • SIP

    protocols.com


    Digital communications rationale
    Digital Communications: Rationale

    • Information Theory:

      • What is the fundamental limit on the compression and refinement of information generated by the source?

      • What is the fundamental limit on the transmission rate of information over a noisy channel?

    • How do we approach these limits?


    Principle
    Principle

    Digital message

    1 1

    1 0 1 0………

    0 0

    Digital

    code

    Analog

    message

    modulate

    1 0 1 0

    Sinusoidal carrier

    AM

    FM

    PM

    AM &

    PM


    Digital communication paradigms

    Message 1

    Message 1

    Multiplexer

    2

    Demultiplexer

    1

    2

    3

    1

    S

    2

    3

    S

    Message 2

    Message 2

    Message 3

    Message 3

    3

    H

    H

    1

    Depacket-izing

    Message 1

    2

    H

    Message 1

    3

    H

    H

    1

    Depacket-izing

    Packetizing

    Message 2

    Message 2

    2

    H

    3

    H

    Message 3

    Depacket-izing

    H

    1

    Message 3

    2

    H

    Digital Communication Paradigms

    Circuit Switching

    Sync bits

    Packet Switching

    Header

    bits


    Digital communications transceiver
    Digital Communications Transceiver

    Anti-

    aliasing

    Filter

    Error

    Control

    Encoder

    Data

    Encryption

    Encoder

    Channel/

    Line

    Encoder

    Source

    Encoder

    Sampling

    Quantization

    Modulator

    MUX

    ADC

    Analog i/p

    CODEC

    MODEM

    Multiple access channel

    Analog o/p

    Error

    Control

    Decoder

    Data

    Encryption

    Decoder

    Source

    Decoder

    Audio

    Amp

    Reconstruction/

    DAC

    Equalization /

    Decision

    Circuits

    Demod-ulator

    DEMUX



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